PT symmetry in a fractional Schrödinger equation
By Yiqi Zhang, Hua Zhong, Milivoj R. Belic, Yi Zhu, Wei-Ping Zhong, Yanpeng Zhang, Demetrios N. Christodoulides, M. Xiao. 2016
149 citations recorded by the source corpus.
We investigate the fractional Schrödinger equation with a periodic ‐symmetric potential. In the inverse space, the problem transfers into a first‐order nonlocal frequency‐delay partial differential equation. We show that at a critical point, the band structure becomes linear and symmetric in the one‐dimensional case, which results in a nondiffracting propagation and conical diffraction of input beams. If only one channel in the periodic potential is excited, adjacent channels become uniformly excited along the propagation direction, which can be used to generate laser beams of high power and narrow width. In the two‐dimensional case, there appears conical diffraction that depends on the competition between the fractional Laplacian operator and the ‐symmetric potential. This investigation may find applications in novel on‐chip optical devices.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6dfe835538966d25e57f421bfe6ad71e2c1c48d9
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Statistical and Nonlinear Physics
Citations in the corpus
- Optical Solitons and Vortices in Fractional Media: A Mini-Review of Recent Results (2021, unknown): “Realization of the propagation dynamics of light beams governed by this equation was proposed in Reference [14], followed by its extension for models including complex potentials subject to the condition of the parity-time (PT ) symmetry [15,16].”
- Inequalities by Means of Generalized Proportional Fractional Integral Operators with Respect to Another Function (2019, methodology): “Besides, our outcomes are practically identical to equality-time evenness in a fractional Schrödinger equation [20] and proliferation elements of light beam in a fractional Schrödinger equation [21].”
- A Solution for Volterra Fractional Integral Equations by Hybrid Contractions (2019, background): “[14] investigated the dynamics of waves in the FSE with a PT -symmetric potential.”